Results 191 to 200 of about 4,079 (208)
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Centralizers and Jordan triple derivations of semiprime rings
Communications in Algebra, 2018Let R be a semiprime ring with extended centroid C and with maximal left ring of quotients . An additive map is called a Jordan triple derivation if for all . In 1957, Herstein proved that a Jordan triple derivation, which is also a Jordan derivation, of
Tsiu-Kwen Lee, T. Quynh
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On the Adjoint Group of Semiprime Rings
Communications in Algebra, 2006An associative ring R, not necessarily with a unity, is called semiprime if it has no nonzero nilpotent ideal. It is proved that in the adjoint group of a semiprime ring R every soluble-by-finite normal subgroup centralizes the Jacobson radical of R. In particular, if R is a semiprime ring with unity, then the same result holds for the multiplicative ...
CATINO, Francesco +2 more
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On centralizer of semiprime inverse semiring
, 2016Let S be 2-torsion free semiprime inverse semiring satisfying A2 condition of Bandlet and Petrich [1]. We investigate, when an additive mapping T on S becomes centralizer.
S. Sara, M. Aslam, M. A. Javed
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On Derivations in Semiprime Rings
Algebras and Representation Theory, 2011Let R be a ring, S a nonempty subset of R and d a derivation on R. A mapping \(f:R\longrightarrow R\) is called commuting on S if [f(x),x] = 0 for all x ∈ S. In this paper, our purpose is to produce commutativity results for rings and show that if R is a 2-torsion free semiprime ring and I a nonzero ideal of R, then a derivation d of R is commuting on ...
Huang Shuliang, Shakir Ali
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Israel Journal of Mathematics, 1975
LetG be a finite group of automorphisms acting on a ringR, andRG={fixed points ofG}. We show that under certain conditions onR andG, whenRGis semiprime Goldie then so isR. In particular, ifa∈R is invertible andan∈Z(R), thenRG,withG generated by the inner automorphism determined bya, is the centralizer ofa—CR(a).
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LetG be a finite group of automorphisms acting on a ringR, andRG={fixed points ofG}. We show that under certain conditions onR andG, whenRGis semiprime Goldie then so isR. In particular, ifa∈R is invertible andan∈Z(R), thenRG,withG generated by the inner automorphism determined bya, is the centralizer ofa—CR(a).
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Prime and semiprime inner functions
Journal of the London Mathematical Society, 2013International ...
Gorkin, Pamela +2 more
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Functional equations related to higher derivations in semiprime rings
, 2021O. H. Ezzat
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Mathematical Notes, 1995
It is proved that a right distributive semiprime PI ringA is a left distributive ring and for each elementx ∈A there is a positive integern such thatx n A=Ax n . We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive ...
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It is proved that a right distributive semiprime PI ringA is a left distributive ring and for each elementx ∈A there is a positive integern such thatx n A=Ax n . We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive ...
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On Prime and Semiprime Rings with Derivations
Algebra Colloquium, 2006Let R be a ring and S a nonempty subset of R. A mapping f: R → R is called commuting on S if [f(x),x] = 0 for all x ∈ S. In this paper, firstly, we generalize the well-known result of Posner related to commuting derivations on prime rings. Secondly, we show that if R is a semiprime ring and I is a nonzero ideal of R, then a derivation d of R is ...
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A note on multiplicative (generalized)-derivations and left ideals in semiprime rings
, 2020B. Dhara, S. Kar, Swarup Kuila
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